Method of grinding gear shaper cutters



June 13, W67 F. KENDALL. 3,324,604

METHOD OF GRINDING GEAR SHAPER CUTTERS Filed July 30, 1964 2 Sheets-Sheet 1 Fl [5.5 INVENTOR.

LLOYD F. KENDALL BY m5 ATTORNEY June R3, 1967 L. F. KENDALL 3,324,604

METHOD OF GRINDING GEAR SHAPER CUTTERS Filed July 30, 1964 2 Sheets-Sheet 2 INVEN TOR. LLOYD F KE NDAL L.

Hls ATTORNEY FIE-1.7

3,324,604 METHQD F GRINDING GEAR SHAPER CUTTERS Lloyd 1F. Kendall, Springfield, Vt, assignor to The Fellows Gear Shaper Company, Springfield, Vt. Filed July 30, 1964, Ser. No. 386,355 4 Claims. (Cl. 51288) The present invention relates to gear shaper cutters and in particular, to a new and novel method of grinding such gear shaper cutters and the like.

Gear shaper cutters of the well known Fellows type and in particular, cutters which have chamfering portions or other portions thereon which are modified from the active involute are the subject matter of the present invention. Such cutters are shown in U.S.' Patent No. 1,610,571, issued Dec. 14, 1926, to E. W. Miller and also in my prior US Patent No. 2,801,459, issued Aug. 6, 1957.

Cutters of this type have teeth located on their periphery and are conjugate to the gears that these cutters form and are similar in appearance to such gears. The present method of grinding is related particularly to involute spur and helical cutters, either external or internal, and in particular to so-called modifying type cutters.

The inventions of the Miller patent and my own prior patent were attempts to secure cutters which would retain a constant relation between the modified portion of the cutter teeth and the true active involute of the teeth throughout the life of the cutter, but the maintenance of this constant relationship was somewhat limited during the repeated sharpening and grinding back of cutters constructed in accordance with the inventions of these patents. In my present invention, this constant relation throughout the life of the cutter is limited only by the necessity of providing sufiicient thickness of the cutter teeth so as to furnish strength enough to sustain the teeth during the cutting of a gear.

Cutters ground according to the method of the present invention as described hereinafter will have a much longer wearing life than any cutters in the art heretofore,

The wearing life of cutters ground by the present invention will be governed only by the geometry of said cutter and the geometry of the work it cuts and by the strength factor, rather than by the apparatus which grinds said cutter which has been a factor in the past.

The modifiedportion of all cutters ground according to the method contained herein will remain exactly the same throughout the many necessary repeated sharpenings and will not deviate in relation to the side face curves of the teeth any amount between the first and last sharpening during the full life of the cutters.

In fact, the geometry of grinding cutters by this method produces gear shaper cutters which hold a true relationship between the active involute and any modified portion thereon between the first and last sharpening throughout the full life of the cutter.

For simplicity, the invention is shown as applied to spur gears in the present drawings and specification, but as will be obvious, can be applied equally as well to either spur or helical gears and internal spur or helical gear shaper cutters.

Obviously the present invention can be applied to helical gear shaper cutters of either left or right hand lead by the application of additional geometric equations well known in the art.

cutters since all spur cutters must have a slight lead on each side of each tooth. This lead is of a degree sufficient to obtain the side clearance necessary to obtain proper cutting action,

Theref ore the principal object of the present inven- 3,324,604 Patented June 113, 1967 tion is to provide a method of grinding gear shaper cutters in which the maximum useful life of the cutter can be determined by the geometry of the cutter and the Work rather than by the apparatus which grinds the cutter.

Another object of the present invention is to provide a method of grinding gear shaper cutters which have a modified chamfering portion that remains exactly in the proper relation to the active involute and is the same at all planes of the cutter as it is ground back through its useful full life. i

Another object of the present invention is to provide a method of grinding gear cutters which retain a true involute and related modified portion at any plane of the cutter during the sharpening back of said cutter through its useful tool life.

In the present invention the teeth are formed by a rotating grinding wheel which is reciprocated relative to the cutter teeth to be ground along a certain prescribed path which is determined as set forth below in such a manner that the correct relation of both modified portions of the cutter teeth and the true involute of the cutter teeth will remain constant throughout the active tool life.

The modified portions of present day gear shaper cutters may be considered as involutes which are determined from different base circles than that from which the main involute of the cutter is generated.

Various base circles on the cutter being ground are the source of origin from which the various involutes of such a cutter are determined.

The path of travel of a rotating grind wheel can best be thought of as stroking along a given path while the work or gear cutter being ground is rolled over the top of the periphery of the moving grinding wheel while one side of each tooth is being ground. While the grinding wheel passes by the cutter being ground it shapes the contour of the tooth which includes an involute curve and one or more modifying portions. After the tooth has rolled over the wheel the gear is then indexed and one side of the next adjacent tooth is brought into contact with the grinding wheel while it makes its next stroking pass and so on until all the teeth of the cutter are ground to the shape desired.

The travel of the grinding wheel relative to the cutter grinds a cutting tooth having an involute profile and modified portions capable of cutting the type of gear desired.

In grinding a gear shaper cutter to be used in cutting spur gears, the axis of the grinding wheel is substantially perpendicular to the axis of the cutter to be ground, but it is disposed at a sufficient angle to such a perpendicular as is necessary to obtain the desired side clearance on the cutter. In grinding a gear shaper cutter to be used in cutting helical gears this angular disposition of wheel and cutter must be increased by the amount of helix which the cutter is to cut on a given work gear when in use.

When the cutter is being ground it is necessary, if the cutter is to maintain the proper shape on a work gear after the cutter is ground when becoming dull, to vary the penetration of the grinding wheel into the cutter. This variation must follow a definite curve which is determined from the change in the center distances between work and cutter which is necessary when the cutter is in use and as it is ground back. This curve is generally concave when All spur cutters can be considered, in essence, helical viewed from the axis of the cutter when the cutter is to be used in cutting an external work piece and is generally convex when viewed from the axis of the cutter when the cutter is to be used in cutting an internal gear.

The cutter being ground andconcerned with this invention is of the type shown in the two patents referred to above but by use of the method with which this applicationis concerned, it is possible to obtain a much increased tool life and to regrind the cutter many more times and its life is limited only by extraneous factors which are not concerned with maintaining the proper tooth proportions and sharpness throughout the life of the cutter.

In the drawings: v

FIG. 1 shows a sectional view of a cutter being ground by a grinding wheel of the type concerned with the present invention and the relation of the cutter and a gear to be cut by the cutter. The outside angle A is of inconsequential value in relation to the formula, but here designates the outside clearance of such cutters well known in the art.

FIG. 2 is a section along line 2-2 of FIG. 1 and showing particularly the ch'amfer or modified portion of the gear tooth.

FIG. 3 is a cutaway section of a gear shaper cutter ground according to the present method and illustrating a single tooth and the curve EE along which the modifled root portion of the tooth is formed.

FIG. 4 is a sectional view along line 44 of FIG. 1 showing a section of the grinding wheel and a portion of a gear shaper cutter being ground.

FIG. 5 is a partial view showing the grinding wheel and the tooth of a cutter being ground and illustrating the progressively increased infeed of the grinding wheel, and also illustrating the curve EE along which the wheel is fed.

FIG. 6 is a view showing the geometry and method used to determine the correct center distances between the cutter and the work at planes A, B and C of the cutter.

FIG. 7 is aview showing the geometry used in correctly locating the modified portion of the cutter in various planes of the cutter as it is sharpened back from plane A to plane B to plane C.

Like reference characters designate the same parts and elements wherever they occur in all the figures.

The basis of the present invention lies in calculating the ,path of curve EE shown in FIG. 3 and FIG. 5 which is the path along which the grinding wheel must be fed into depth to maintain the proper relation between the modified portion of the cutter 1 and the active involute.

In the calculating of curve E-E a factor known as an involute function will be employed which is a term well known in the art and tables of such functions are available in numerous textbooks. An example of one such book is Spur Gears by Earle Buckingham.

Curve EE is calculated and established by finding a series of coordinates which will be designated hereinafter as X and coordinates.

As stated above, the chamfer on the work 2 is given an involute shape in present day practice. The various otherelements of the work are not of importance insofar as the present invention is concerned. However, three elements on the work do affect the calculation of curve Two of these are the base diameter from which the involute chamfer originates known as the base diameter of the cham fer and designated as CBD and the diameter at which the chamfer intersects the active involute and designated as D These two elements are not shown on the drawings. The third element is the angle which is formed by a line sloping with the chamfer and designated as G and a radial line on the work drawn through the point of intersection of the chamfer and the activeinvolute and hereinafter designated as the C angle as shown in FIG. 2.

It has been found that: CBD D cos C I The base diameter-from which the involute chamfer on the-cutter is formed is designated as CBD and this can be calculated by knowing the number of teeth in the cutter designated as N and the number of teeth in the work and using the formula N XCBD Also in order to define curve EE a value which is designated as Q (see FIG. 6) is necessary. Q is equal to one half the base diameter of the work designated as ED plus one half the base diameter of the cutter designated as BD (both not shown). Therefore:

Variations in center distance between cutter 1 and work 2 are necessary to secure the desired depth of cut upon cutter sharpening and for the purpose of illustration three different planes of the cutter are shown and are used to determine curve EE. These planes are shown at A, B and C and for the purpose of illustration are taken at new life, half life and full life of the cutter (see FIG. 1).

It will be obvious that the center distance at plane A for example and designated CD will be equal to one half times the outside diameter of the cutter designated as OD not shown in the drawings, plus the diameter at the root of the work teeth designated as RD also not shown, or stated in an equation: CD /2 (OD -I-RD S is considered the active pressure angle between cutter and work and therefore S S and S designate the pressure angles at planes A, B and C of the cutter.

The cosine of the pressure angle (5..) is equal to Q divided by the center distance (CD and therefore:

Q Cosine S g 6) The next step necessary is to find the involute function S S and S from a table such as referred to above. These involute functions will be referred to below as Inv S Inv S and Inv S The involute face of the cutter is displaced relative to the base circle as the cutter is ground back due as is obvious, to the tapering of the cutter tooth which is necessary to obtain the side clearance for proper cutting action. The symbol U represents this displacement (see FIG. 6).

The involute function of S at plane B is equal to the involute function of S at plane A minus the displacement due to the taper divided by two times Q or expressed mathematically:

v The involute function of the pressure angle at plane C is equal to the involute function of the pressure angle at plane A minus two times the involute function of U at plane B or: Inv S =Inv S 2 Inv U The center distance between cutter and work at plane B is equal to Q divided by the cosine of the pressure angle at plane B or:

C0sine S Similarly the center distance at plane C can be calculated as:

Cosine S S, is the active pressure angle between cutter and work as determined with respect to the chamfering or modifying portion of the cutter and work. Q is the equivalent of 'Q but is determined with respect to the base diameters of cutter and work from which the involutes of the 'chamfer or modified portions are developed.

Therefore the cosine of S means the cosine of the pressure angle with respect to the chamfering base circle at plane A is equal to Q divided by the center distance at plane A or:

Q1 Cosine S Similarly:

Cosine S Cosine S As was the case with respect to the active involute the involute function of the pressure angles of the modifying involute portion of the cutter must be determined and will be designated as Inv S Inv S and Inv S re spectively at planes A, B and C.

As shown in FIG. 7, U represents the displacement due to the taper or side clearance and as is similar to the symbol U, but is the taper with respect to the chamfering or modifying portion of the cutter.

Therefore the formula form is similar to the method employed in determining the value of U:

U is the distance between the involute side faces at plane A and plane B as said involutes have been originated from the base circle of the chamfering portion of the cutter.

U is equal to Q times the involute function of the pressure angle at plane A, here again the pressure angle being taken from the chamfering base circle, minus the involute function of the pressure angle at plane B or mathematically expressed: U =Q (Inv S -Inv S In FIG. 7 the dotted line R represents the position of the involute chamfering portion which is obtainable by present known methods of gear shaper cutter grinding. The line R is the position of the involute which is obtained by the method of the present invention. Therefore it will be seen that the distance PU is the correction obtained by the method of grinding herein concerned. It will be seen from FIG. 7 that: PU /2 U U A cutter ground by the present method will have the involute chamfer or modifying portion at plane B in the position shown at center distance CD and at plane C this modifying portion will be at OD Such cutter will maintain this modifying portion in the correct position as related to the active involute and the change in center distance in all planes.

In FIG. 4 the disposition of the gear shaper cutter and grinding wheel are shown when the cutter is being ground. As is well known in the art, the cutter is mounted on a slide and this slide is fed along a line P-P which is disposed at an angle T to axis O O of the grinding wheel about which the wheel is rotated.

The line LL is the slope line of the chamfering portion of the wheel taken in a transverse plane as shown by line 44 of FIG. 1. The line M-M is perpendicular to the line P-P and W is the angle between line LL and line M-M.

The line N is shown along the face of the wheel which generates the active involute of the cutter. W, designates the angle between the line L-L and line N.

The cosine of angle W is equal to Q times the cosine of angle T divided by Q or:

Angle W is equal to angle W minus angle T or:

W =WT As seen in FIGS. 3 and 5 the distance X is the amount of relative infeed to be given to the grinding wheel 3 as it traverses the cutting tool from plane A to plane B.

The X and X illustrated in FIG. 5 shows the distance the grinding wheel W climbs in order to create curve EE in the root as it travels from front to back of a cutter being ground. An inconsequential correction to the X and X can obviously be obtained in relative practice.

The value of U divided by the cosine of W mnius one half of U multiplied by the cotangent of W is equal to X or:

r mb K -cotangent W (m 2 X in FIGS. 3 and 5 is similar to X but represents the It will be noted that the two formulas differ in that in one case the last U is divided by two and in the second case it is not. This is by reason of the fact that the X is taken at half life of the cutter and X is taken at full life. If other points were taken to determine curve E-E the value of U would be determined proportionately.

In FIG. 3, Y is the linear distance from plane A to plane B measured parallel to the cutter aXis. Y is the distance from plane A to plane C.

As shown in FIG. 1 the grinding wheel axis K is set at an angle to the axis Z of the cutter. In the case of spur cutters this is due to the necessity of obtaining the desired side clearance and in the case of helical cutters, this angle is in addition affected by the helix angle of the gear to be cut. In FIG. 1 this angle is designated as MS and is known as the machine setting angle.

. The tangent of the machine setting angle (MS) is equal to U (FIG. 6) divided by the distance Y or:

U Tangent M S In FIGS. 1 and 5, Y is the distance from plane A to plane B measured in the direction of the machine setting angle. Y is equal to the distance Y divided by the cosine of the machine setting angle or:

Yb Cosine Ms Similarly, Y is the distance from plane A to plane C in the direction of the machine setting angle and therefore:

Y and Y show the distances the wheel must be relatively traversed in relation to the infeed of the wheel. X {and Y then X and Y determine points which the curve EE must intersect if the chamfer or modifier is to maintain the proper relation to the active involute throughout the full life of the cutter and many sharpenings. In actual practice it would be desirable to calculate additional coordinates in order to more accurately determine the shape of curve EE and the selection of only two positions of the relation of cutter and grinding wheel have been described herein for purposes of illustration only.

The tangent of the grinding wheel chamfer angle J (FIG. 5) is equal to the tangent of the (W times the cosine of the machine setting angle (MS angle) Tan J=tan W cos MS angle What I claim and desire to secure by Letters Patent is:

1. The method of forming gear shaper cutters in which said cutters have peripherally disposed longitudinally extending teeth thereon which teeth have side faces having an active involute and a modified portion intersecting said active involute which comprises rolling said cutter past a rotating forming tool to generate said active involute and said modified portion, relatively reciprocating said forming tool lengthwise of the teeth on said cutter, relatively feeding said forming tool depthwise of the teeth on said cutter during said reciprocating movement along a predetermined curved path, said path being of such a curvature so that it corresponds to the amount of depth feed necessary to maintain said active involute and 7 said modified portion in the same relative position from the leading face of said cutter teeth to the active trailing portion of said teeth.

2. The method of grinding a gear shaper cutter to be used in cutting a gear having teeth thereon that are modified by having tipswhich deviate in part from a true active involute, said cutter having a series of peripherallly spaced longitudinally disposed tapered teeth thereon, which teeth have side faces with an active involute and a modified portion intersecting said involute and said teeth being conjugate to the teeth of said gear which comprises rolling said cutter in engagement with a rotating grinding wheel to generate said active involute and said modified portion, relatively reciprocating said grinding wheel lengthwise of the teeth on said cutter simultaneously with said rolling movement feeding said grinding wheel depthwise of the teeth on said cutter during said reciprocating movement, said feeding movement being made in timed relation to said reciprocation so that said grinding wheel follows a predetermined curved path relative to said cutter teeth, the curvature of said path being such that the relation of the active involute and the modified portion of said cutter teeth remains constant throughout the life of the cutter.

3. The method of grinding a gear shaper cutter of the type having a series of peripherally disposed teeth thereon which teeth extend substantially in the direction of the axis of said cutter and which teeth are tapered both longitudinally and inwardly with respect to the axis of said cutter and which teeth have flanks which have a true active involute and a chantfering portion intersecting said active involute thereon so that said cutter is adapted to generate a gear having teeth with an active operating involute and a relieved tip portion which comprises rollingsaid cutter in engagement with and against the side face of a rotating grinding wheel so that the teeth of said cutter will be formed conjugate to the shape of the grinding Wheel, which wheel has a flat side face and a portion adjacent its periphery modified from said flat face, reciprocating said wheel lengthwise of said cutter in timed relation to said rolling movement, relatively feeding said grinding wheel depthwise of said cutter teeth towards the axis of said cutter in timed relation to said reciprocation, said feeding being made along a predetermined curved path relative to said cutter teeth, the curvature of said path being such that the relationship between the true active involute on the cutter and the chamfering portion remains constant throughout the life of the cutter whereby said cutter will produce gears of the same characteristics when the cutter is ground back after repeated use.

4. A method according to claim 3 in which said curve is determined from a base point on the leading face of the cutter, at half life of the cutter it passes through a point displaced vertically from the base point a distance determined by multiplying the cotangent of the slope line as taken in a transverse plane by the displacement of the chamfering portion at said half life divided by the cosine of the slope line as taken in a transverse plane minus the displacement of the involute due to the taper divided by two and where the horizontal distance of said point from the face of the cutter is equal to the linear distance from the face of the tooth at the one half life plane divided by the cosine of the angle which the grinding wheel makes with the axis of the cutter and at full life of the cutter the curve passes through a point which is vertically displaced from the base point a distance which is equal to the cotangent of said slope line as taken in a transverse plane multiplied by the displacement of the chamfering portion divided by the cosine of said slope line as taken in a transverse plane minus the displacement of the involute and where the horizontal displacement of the point has been moved through a distance equal to the distance of the full face of the cutter at full life divided by the cosine of the angle which the grinding wheel makes with the axis of the cutter.

References Cited UNITED STATES PATENTS 1,610,571 12/1926 Miller 29103 1,910,730 5/1933 Wildhaber 51-55 2,620,599 12/1952 Riley 5156 2,801,459 8/1957 Kendall 2995 LESTER M. SWINGLE, Primary Examiner. 

1. THE METHOD OF FORMING GEAR SHAPER CUTTERS IN WHICH SAID CUTTERS HAVE PERIPHERALLY DISPOSED LONGITUDINALLY EXTENDING TEETH THEREON WHICH TEETH HAVE SIDE FACES HAVING AN ACTIVE INVOLUTE AND A MODIFIED PORTION INTERSECTING SAID ACTIVE INVOLUTE WHICH COMPRISES ROLLING SAID CUTTER PAST A ROTATING FORMING TOOL TO GENERATE SAID ACTIVE INVOLUTE AND SAID MODIFIED PORTION, RELATIVELY RECIPROCATING SAID FORMING TOOL LENGTHWISE OF THE TEETH ON SAID CUTTER, RELATIVELY FEEDING SAID FORMING TOOL DEPTHWISE OF THE TEETH ON SAID CUTTER DURING SAID RECIPROCATING MOVEMENT ALONG A PREDETERMINED CURVED PATH, SAID PATH BEING OF SUCH A CURVATURE SO THAT IT CORRESPONDS TO THE AMOUNT OF DEPTH FEED NECESSARY TO MAINTAIN SAID ACTIVE INVOLUTE AND SAID MODIFIED PORTION IN THE SAME RELATIVE POSITION FROM THE LEADING FACE OF SAID CUTTER TEETH TO THE ACTIVE TRAILING PORTION OF SAID TEETH. 